Q2 of 82 Page 130

By using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 2x3 + 9x2 – 11x – 30 and g(x) = x + 5

Formula used.


If f(x) is a polynomial with degree n


Then (x – a) is a factor of f(x) if f(a) = 0


1st we find out zero of polynomial g(x)


x + 5 = 0


x = – 5


if f(x) is 2x3 + 9x2 – 11x – 30


then putting x = – 5 ;


f( – 5) = 2( – 5)3 + 9( – 5)2 – 11( – 5) – 30


= 2 × ( – 125) + 9 × (25) – 11x( – 5) – 30


= – 250 + 225 + 55 – 30


= 0


Conclusion.


∴ g(x) is a factor of f(x)


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